Direct Variation - Math Lab

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically expressed as y = kx, where k is a non-zero constant.

Front

How do you determine if a graph represents a direct variation?

Back

A graph represents direct variation if it is a straight line that passes through the origin (0,0).

Front

If y varies directly with x and y = 39 when x = 3, what is the constant of variation (k)?

Back

The constant of variation (k) is 13, calculated as k = y/x = 39/3.

Front

If a job pays $70 for 5 hours of work, how much will it pay for 1 hour?

Back

It will pay $14 for 1 hour, calculated as $70/5 hours.

Front

If a tutor earns $222 for 10 hours of work, how much will they earn for 35 hours?

Back

They will earn $777 for 35 hours, calculated as (222/10) * 35.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

How do you find the value of y when x is given in a direct variation problem?

Back

To find the value of y, use the formula y = kx, substituting the known value of x and the constant k.

Front

What does it mean if a graph is a straight line but does not pass through the origin?

Back

It means that the relationship is not a direct variation; it may be a linear relationship but not proportional.

Front

In a direct variation, if y = 26 when x = 2, what is the value of k?

Back

The value of k is 13, calculated as k = y/x = 26/2.

Front

If 15 miles is represented by 3 centimeters on a map, how many centimeters represent 135 miles?

Back

27 centimeters represent 135 miles, calculated using the ratio (3 cm/15 miles) = (x cm/135 miles).